Check to make sure you don't have more than 50 unread emails in your Office 365 inbox. If you have more than 50 unread emails in your inbox, you will need to clear it out before the Aero sync will work.
Log into your Office 365 account online (not Outlook on your desktop)
Click on your Inbox
Click on the filter dropdown and choose Unread.
Check the box next to Inbox to select all. You will see 'XX Conversations selected' with some options. Choose Mark as read.
Once you've cleared out your inbox, you may want to know how to delete all those "overflowing inbox" messages. Here's how.
Check that your Aero account is connected to the correct Office 365 account. Make sure it's actually an Office 365 account- not an Outlook Exchange account. Aero does not sync with Outlook Exchange.
Check to make sure you have entered the correct Office 365 email and password. Note that your Office 365 email may be different that the email address you use to log into Aero. To edit the Office 365 information, navigate to Work > My Preferences and click the Disconnect from Office 365 button. On the next screen, you can edit the Office 365 email and password.
Check to make sure you have told Aero to check your email:
Navigate to Work > My Preferences > Email Settings
If you want Aero to automatically check for email, check the Auto Update Email box
Make sure that EITHER Send & Receive Email OR Send Email Only is checked
More on the email settings: Connecting Aero to Office 365
Check to make sure that you have unread email in your inbox from email addresses that are listed in your Aero Account.